Radial distribution function of a hard-sphere fluid for the nearest neighbor surroundings

An expression for RDF as a function of two variables, the distance r and the packing factor eta, was obtained by approximating the results of Monte Carlo simulation of a hard-sphere fluid. The mean square accuracy of the expressions presented is about +/- 0.0002 (1 <= r <= 1.5, 0 <= eta <= 0.5). A continuous extension of RDF to the region of r < 1 is proposed, which provides the continuity of the first and second derivatives of RDF at the point r = 1. Analysis of the problem of determining the hard sphere diameter in WCA theory of simple liquids shows that the proposed expression makes it possible to directly calculate the hard sphere diameter without any simplifying approximations.